Hi FISers,
I think information and energy are inseparable in reality. Hence to understand
what information is, it may be helpful to understand what energy (and the
associated concept of motion) is. In this spirit, I am forwarding the
following email that I wrote motivated by the lecture given by Dr. Grossberg
this afternoon at the 119th Statistical Mechanics Conference. In Table 1 in
the email, I divided particle motions studied in physics and biology into three
classes -- (i) random, (ii) passive, and (iii) active, and identified the field
of specialization wherein these motions are studied as (i) statistical
mechanics, (ii) stochastic mechanics, and (iii) info-statistical mechanics.
The last term was coined by me in 2012 in [1]. I will be presenting a short
talk (5 minutes) on Info-statistical mechanics on Wednesday, May 9, at the
above meeting. The abstract of the short talk is given below:

Short talk to be presented at the 119th Statistical Mechanics Conference,
Rutgers University, Piscataway, N.J., May 6-9, 2018).
Planckian Information may be to Info-Statistical Mechanics what Boltzmann
Entropy is to Statistical Mechanics.
Sungchul Ji, Department of Pharmacology and Toxicology, Ernest Mario School of
Pharmacy, Rutgers University, Piscataway, N.J. 08854
Traditionally, the dynamics of any N-particle systems in statistical mechanics
is completely described in terms of the 6-dimensional phase space consisting of
the 3N positional coordinates and 3N momenta, where N is the number of
particles in the system [1]. Unlike the particles dealt with in statistical
mechanics which are featureless and shapeless, the particles in biology have
characteristic shapes and internal structures that determine their biological
properties. The particles in physics are completely described in terms of
energy and matter in the phase space but the description of the particles in
living systems require not only the energy and matter of the particle but also
their genetic information, consistent with the information-energy
complementarity (or gnergy) postulate discussed in [2, Section 2.3.2]. Thus,
it seems necessary to expand the dimensionality of the traditional phase space
to accommodate the information dimension, which includes the three coordinates
encoding the amount (in bits), meaning (e.g., recognizability), and value
(e.g., practical effects) of information [2, Section 4.3]. Similar views were
expressed by Bellomo et al. [3] and Mamontov et al. [4]. The expanded “phase
space” would comprise the 6N phase space of traditional statistical mechanics
plus the 3N information space entailed by molecular biology. The new space (to
be called the “gnergy space”) composed of these two subspaces would have 9N
dimensions as indicated in Eq. (1). This equation also makes contact with the
concepts of synchronic and diachronic informations discussed in [2, Section
4.5]. It was suggested therein that the traditional 6N-dimensional phase space
deals with the synchronic information and hence was referred to as the
Synchronic Space while the 3N-dimensional information space is concerned with
the consequences of history and evolution encoded in each particle and thus was
referred to as the Diachronic Space. The resulting space was called the gnergy
space (since it encodes not only energy but also information).
Gnergy Space = 6N-D Phase Space + 3N-D Information Space
(1)
(Synchronic Space)
(Diachronic Space)
The study of both energy and information was defined as “info-statistical
mechanics” in 2012 [2, pp. 102-106, 297-301]. The Planckian information of the
second kind, IPS, [5] was defined as the negative of the binary logarithm of
the skewness of the long-tailed histogram that fits the Planckian Distribution
Equation (PDE) [6]. In Table 1, the Planckian information is compared to the
Boltzmann entropy in the context of the complexity theory of Weaver [8]. The
inseparable relation between energy and information that underlies
“info-statistical mechanics” may be expressed by the following aphorism:
“Information without energy is useless;
Energy without information is valueless.”
Table 1. A comparison between Planckian Information (of the second kind) and
Boltzmann entropy. Adopted from [6, Table 8.3].
Order
Disorder
IPS = - log2 [(µ - mode)/σ]
(2008-2018)
S = k log W
(1872-75)
Planckian Information
Boltzmann entropy [7]
Organized Complexity [8]
Disorganized Complexity [8]
Info-Statistical Mechanics [2, pp. 102-106]
Statistical Mechanics [1]
References:
[1] Tolman, R. C. (1979). The Principles of Statistical Mechanics, Dover
Publications, Inc.,
New York, pp. 42-46.
[2] Ji, S. (2012) Molecular Theory of the Living Cell: Concepts, Molecular
Mechanisms, and
Biomedical Applications. Springer, New York.
[3] Bellomo, N., Bellouquid, A. and Harrero, M. A. (2007). From microscopic
to macroscopic
descriptions of multicellular systems and biological growing tissues. Comp.
Math. Applications
53: 647-663.
[4] Mamontov, E., Psiuk-Maksymowitcz, K. and Koptioug, A. (2006).
Stochastic mechanics
in the context of the properties of living systems. Math. Comp. Modeling
44(7-8): 595-607.
[5] Ji, S. (2018). Mathematical (Quantitative) and Cell Linguistic
(Qualitative) Evidence for
Hypermetabolic Pathways as
[SJ1]<file:///C:/Users/sji/Dropbox/SMC_2018/Ji_Spring_2018.docx#_msocom_1>
Potential Drug Targets. J. Mol. Genet. Medicine (in press).
[6] Ji, S. (2018). The Cell Language Theory: Connecting Mind and Matter.
World Scientific
Publishing, New Jersey. Chapter 8.
[7] Boltzmann distribution law.
https://en.wikipedia.org/wiki/Boltzmann_distribution.
[8] Weaver, W. (1948) Science and Complexity. American Scientist 36:536-544.
- - - - - - - - - - - - - -the Email to Dr. Grossberg --------------------- - -
- --- - -- - - - - - - - - - - - - -
________________________________
Hi Dr. Grossberg,
Thank you for your thought-provoking lecture (entitled "From Sisyphus to
Boltzmann: an example of repulsive depletion interaction") this afternoon at
the 119th Statistical Mechanics Conference at Rutgers.
Your lecture prompted me to construct the following table based on my
experience as a theoretical cell biologist over the last 4 decades as
summarized in [1, 2].
According to Table 1, we can recognize three distinct kinds of particle motions
in physics and biology that may be studied in 3 distinct fields of
specialization, tentatively identified with (i) statistical mechanics, (ii)
stochastic mechanics, and (iii) what I recently referred to as
"info-statistical mechanics" [1,pp. 102-107; 2, pp. 371-374].
Table 1. The trichotomy of particle motions in physics and biology
Particle Motions
(Discipline)
Random motion (1)
(Statistical mechanics)
Passive motion (2)
(Stochastic mechanics ?)
Active motion (3)
(Info-statistical mechanics ?)
[1, 2]
Energy Source
homogeneous thermal environment
external
(e.g., magnetic field)
internal
(e.g., chemical reactions)
Physics
dust particles in water
at equilibrium
dust particles in water in flow
a piece of sodium metal in water at equilibrium
Brownian motion
e.g., Orenstein-Uhlenbeck process
artificial molecular machines
Biology
dead bacteria in water at equilibrium
live bacteria moving down a gradient
live bacteria swimming against a gradient
Brownian motion
diffusion driven by gradient
Chemotaxis driven by ATP hydroly
* In your lecture today,. you referred to "active motions" of inanimate
particles, which seems to correspond to "passive motions" in the above table,
since the driving force for your particle motion is external to the particle.
If you wish to preserve the term "active motion", it seems to me necessary to
differentiate between the "externally driven active motion" and the "internally
driven active motion". On the other hand, if we adopt the terms,"active" vs.
"passive" particle motions, we have a precedence in biology where "active
transport" (e.g., the Na/K pump) and "passive transport" (e.g., the Na/Ca
exchange channel) are well known. In fact, the triadic classification of
particle motions defined in Table 1 can be applied to ion movements across
biomembranes with an equal force.
If you have any questions or comments on the suggestions made in Table 1, I
would appreciate hearing from you.
All the best.
Sung
References:
[1] Ji, S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular
Mechanisms, and Biomedical Applications. Springer, New York.
[2] Ji, S. (2018). The Cell Language Theory: Connecting Mind and Matter.
World Scientific Publishing, New Jersey.
With all the best.
Sung